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General existence principles for nonlocal boundary value problems with $$\phi$$-Laplacian and their applications. (English) Zbl 1147.34007
The paper gives general existence principles that can be applied for a large class of nonlocal boundary value problems of $$\phi$$-Laplacian type, namely
$(\phi(x'))' = f_1(t,x,x') + f_2(t,x,x')F_1x + f_3(t,x,x')F_2x,$
$\alpha(x)= 0=\beta(x),$ where the functions $$f_j$$ satisfy local Carathéodory conditions, and may have singularities in their phase variables, $$F_i:C^1[0,T]\to C^0[0,T]$$ and $$\alpha,\beta:C^1[0,T]\to \mathbb R$$ are continuous. Proofs are based on the Leray-Schauder degree theory and use regularization and sequential techniques. Applications and an example are given for some singular boundary value problems.

##### MSC:
 34B15 Nonlinear boundary value problems for ordinary differential equations 47N20 Applications of operator theory to differential and integral equations
##### Keywords:
nonlocal boundary value problems; $$\phi$$-Laplacian
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##### References:
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